The present invention relates to a heterodyne interferometer arrangement, a heterodyne interferometric metering method, and an arrangement for detecting the non-linearity of a heterodyne interferometer, as well as a method of detecting the non-linearity of a heterodyne interferometer.
The basic set-up of a heterodyne interferometer arrangement, which is also referred to as a two-frequency interferometer arrangement, is shown in FIG. 18. The heterodyne interferometer arrangement as a whole is indicated by reference numeral 1 and includes a light source LS for generating light beams E.sub.1, E.sub.2 having a first frequency f.sub.1 and a second frequency f.sub.2. The two beams produced by the light source LS can be described as plane waves, which can be expressed by the following equations: EQU E.sub.1 =E.sub.0 sin (2.pi.f.sub.1 t+.phi..sub.01) (1a) EQU E.sub.2 =E.sub.0 sin (2.pi.f.sub.2 t+.phi..sub.02) (1b)
In the light path after the light source LS, a first beam splitter BS1 is arranged, said beam splitter supplying the light produced by the light source LS to an optical reference branch RB on the one hand and to an optical measuring branch MB on the other. An interferometer unit IF having a structure which is known per se is arranged after the first beam splitter BS1 in the measuring branch MB, said interferometer unit IF including, in turn, a first polarizing beam splitter PB1 followed by first and second interferometer arms A1, A2 in orthogonal directions. As is, in principle, known to the person skilled in the art, each interferometer arm A1, A2 is terminated by a mirror MR1, MR2, which can, for example, be formed by a prism. The two interferometer arms A1, A2 have a first optical length n.sub.1 .multidot.l.sub.1 and a second optical length n.sub.2 .multidot.l.sub.2. At least one of the two interferometer arm lengths corresponds to the quantity to be measured by the heterodyne interferometer arrangement.
At the optical output of the interferometer unit IF, a first polarization filter PF1 is arranged whose polarizing direction is rotated by 45.degree. relative to the directions M.sub.1, M.sub.2 of the two plane waves E.sub.1, E.sub.2. An optoelectric measuring transducer unit in the form of a photodiode D.sub.m is arranged after this first polarization filter PF1.
A second polarization filter PF2 is arranged in the reference branch RB in the light path after the first beam splitter BS1, the polarization direction of said second polarization filter being, just like that of the first polarization filter PF1, rotated by 45.degree. relative to the directions M.sub.1, M.sub.2 of the two plane waves E.sub.1, E.sub.2. The second polarization filter PF2 is followed by an optoelectric reference transformer means in the form of a photodiode D.sub.r. The reference signal I.sub.r produced by this photodiode D.sub.r satisfies the following equation: EQU I.sub.r .about.E.sub.r.sup.2 .about.I.sub.0 cos[2.pi.(f.sub.1 -f.sub.2)t+.phi..sub.0 ] (1c)
In this connection, the following relationship exists with regard to the amplitude I.sub.0 : EQU I.sub.0 .about.E.sub.0.sup.2 ( 1d)
With regard to the constant phase displacement .phi..sub.0, the following connection exists: EQU .phi..sub.0 =.phi..sub.r1 -.phi..sub.r2 ( 1e)
The measuring signal I.sub.m at the output of the optoelectric measuring transducer unit D.sub.m is defined in accordance with the following equation: EQU I.sub.m .about.I.sub.0 cos[2.pi.(f.sub.1 -f.sub.2)t+.phi..sub.0m +.DELTA..phi.] (2a)
In this equation, .DELTA..phi. represents a phase displacement which can be expressed as follows: EQU .DELTA..phi.=.phi..sub.1 -.phi..sub.2 =4.pi.(n.sub.1 l.sub.1 -n.sub.2 l.sub.2)/.lambda..sub.m ( 2b)
In this equation, .lambda..sub.m represents the mean wavelength. An arbitrary initial phase is .phi..sub.0m =.phi..sub.m1 -.phi..sub.m2.
The measuring signal I.sub.m and the reference signal I.sub.r are supplied to a phase comparison circuit PH, which will form the phase difference between the measuring signal I.sub.m and the reference signal I.sub.r.
As can be seen from equations (1c), (2a) and (2b), the measuring signal I.sub.m is subjected to a phase displacement in comparison with the reference signal I.sub.r, said phase displacement changing in response to changes in the optical path lengths n.sub.1 .multidot.l.sub.1 and n.sub.2 .multidot..sub.1 2 in the first and second arms A1, A2 of the interferometer unit IF. Hence, a length variation in one of the two arms A1, A2 can be detected by measuring a resultant phase difference between I.sub.m and I.sub.r.
If, in the case of one example, the resolution which can be achieved when carrying out a phase measurement is 1.degree., a length resolution of 0.9 nm can be attained for the detection of the displacement of a mirror MR1 and MR2, respectively, in the case of the interferometer shown in FIG. 18. The above-described phase displacement .DELTA..phi. between the reference signal I.sub.r and the measuring signal I.sub.m is shown in FIG. 19. FIG. 20 shows the above-described orthogonal direction of the two partial beams E.sub.1, E.sub.2, as well as the arrangement of the polarization filters PF1, PF2 which are displaced by 45.degree. relative thereto.
However, the above-described derivation of the connection between the phase displacement .DELTA..phi. and a length L.sub.1, L.sub.2 to be measured is only applicable under the ideal condition that only one of the two frequencies f.sub.1, f.sub.2 occurs in each interferometer arm A1, A2. This ideal condition is, however, not met in practice. Due to various influences, mixed frequencies are found in both interferometer arms A1, A2. The causes of such frequency mixtures are, for example, non-orthogonality of the polarization directions M.sub.1, M.sub.2 of the incident waves E.sub.1, E.sub.2, mixing due to elliptic polarization of the incident waves E.sub.1, E.sub.2, mixing due to imperfect optics in the light path before the first polarizing beam splitter PB1 as well as incomplete frequency separation by said first polarizing beam splitter PB1.
These errors result in a non-linear relation between the measured phase difference and the displacement to be measured or the change in the optical length of one of the two interferometer arms to be measured.
The following literature sources are cited with regard to the technological background of the present invention:
Sommargren, G. E.: PA0 A new measurement system for precision metrology PA0 Prec. Eng. 9 (1987), 179-184 PA0 Quenelle, R. C.; Wuerz, L. J.: PA0 A new micrometer-controlled laser dimensional measurement and analysis system. PA0 Hewlett-Packard Journ. 34,4 (1983), 3-13 PA0 Dorenwendt, K.; Probst, R.: PA0 Hochauflosende Interferometrie mit Zweifrequenzlasern PA0 PTB-Mitt. 90, (1980), 359-362 PA0 Reinboth, F.; Wilkening, G.: PA0 Optische Phasenschieber fur Zweifrequenz-Laser-Interferometrie PA0 PTB-Mitt. 93, (1983), 168-174 PA0 Bobroff, N.: PA0 Residual errors in laser interferometry from air turbulence and nonlinearity PA0 Appl. Opt. 26, (1987), 2676-2682 PA0 Sutton, C. M.: PA0 Non-linearity in length measurement using heterodyne laser Michelson interferometry PA0 J. Phys. E 20, (1987), 1290-1292 PA0 Steinmetz, C. R.: PA0 Sub-micron position measurement and control on precision machine tools with laser interferometry PA0 Prec. Eng. 12, (1990), 12-24 PA0 Rosenbluth, A. E.; Bobroff N.: PA0 Optical sources of non-linearity heterodyne interferometers PA0 Prec. Eng. 12, (1990), 7-11
In view of this prior art, it is desirable to further develop a heterodyne interferometer arrangement, as well as a heterodyne interferometric metering technique, in such a way that the measuring linearity error is reduced.